Robust monetary policy, optimal delegation and misspecified potential output

•Central bank faces uncertainty about potential output.•Min-max approach to policy.•A conservative central banker is beneficial if uncertainty increases.

Central banks face uncertainty about potential output. We model optimal monetary policy under discretion in a situation in which the central bank adopts a min-max approach to policy. The case for appointing a conservative central banker who puts a larger weight on inflation stabilization becomes stronger as the central bank's concern about misspecifications increases.